Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

Abstract

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.

9 pages, 9 figures

References in corpus (11)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Disorder in a quantum spin liquid: flux binding and local moment formation
• A $\Gamma$-matrix generalization of the Kitaev model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Three-dimensional topological phase on the diamond lattice
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Exact quantum spin liquids with Fermi surfaces in spin-half models

Cited by in corpus (3)

• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice